New Probabilistic PLS method achieves calibrated uncertainty with exact Stiefel optimization

Researchers Haoran Hu and Xingce Wang have published a new paper, 'Exact Stiefel Optimization for Probabilistic PLS,' which addresses critical bottlenecks in two-view learning models. The work overcomes noise-signal coupling and orthogonality constraints by combining noise pre-estimation, constrained likelihood optimization on the Stiefel manifold, and prediction calibration. Crucially, the proposed noise-subspace estimator attains a signal-strength-independent finite-sample rate that matches a minimax lower bound, while the older full-spectrum estimator is shown to be inconsistent under the same model.

In high-noise synthetic settings and two multi-omics benchmarks (TCGA-BRCA and PBMC CITE-seq), the method achieves near-nominal coverage without post-hoc recalibration, matches Ridge-level point accuracy on TCGA-BRCA at rank r=3, and matches or exceeds PO2PLS on cross-view prediction. The framework also extends to sub-Gaussian settings via optional Gaussianization and provides closed-form standard errors through block-structured Fisher analysis. This work enables practitioners to obtain both interpretable latent factors and reliable uncertainty estimates without expensive recalibration steps.